Majority of pet domestic animals lead a sad, cruel and short life. There are no statistics regarding small species, but you can ask any vet what for tragic cases they meet. The sad aspect is that those owners don´t even realise their cruelty. Zoos, farms and laboratories are frequently checked and are regulated by many laws, zoos are additionally under intentense public scrutiny. But private households can´t be effectively under control, ever.
Be assured that I'm not just referring to industrial livestock farming, even though these animals do represent the majority of animals that "have trouble in captivity (...), have a bad time(sic?) and are denied important behaviours in captivity". Jana was so kind to explicate about the plight of privately kept pets, and I can only confirm what she wrote, and might add that this is only the tip of the iceberg. Maybe some readers of these lines should rethink the husbandry conditions of their very own pets...Even with attempts taking place to improve the situation from a grassroot level in the UK, as pointed by @Pertinax, as well as in other countries, most pets and domestic animals in general (and also the ones kept in modern zoos) usually face worse living husbandry conditions than the majority of elephants or cetaceans or great apes or any of the golden calves of the megavertebrate-fixated zoo entertainment industry. And no @lamna, the majority of domestic animals does not "survive perfectly well", especially when produced for consumption (one way or another).
The majority of the millions of pet owners are law abiding, well meaning/adjusted normal people but when it comes to pet keeping, ignorance of their animals' true needs just seems to be the norm. If you explained the shortcomings, most of them would be mortified, but there are no rulings about such issues- its a case of just do what every one else does. Of course nowadays the cages for ferrets, rodents, some small birds etc are often much bigger and fancier than they used to be- a marketing ploy as they cost a lot more to buy- and that does help the inmates to have a somewhat improved life. 
Most of them haven't got the slightest clue.
Some pet chain stores in the UK now will not sell small-sized hutches for rabbits or guinea pigs, another step in the right direction. The latest publicity on rabbit care says hutches should be of sufficient length to allow 'three hops' and even then a larger attatched run should be an essential, as well as rabbit company. Apparently the simple 'rabbit hutch' was a Victorian innovation for keepng rabbits for a short period before being killed for their meat. That system then got extended into pet rabbit-keeping generally. Again selling larger runs and houses should benefit the pet stores as well as the animals, as the bigger they are, the more expensive they are to buy...
One of my pet(sorry for the pun) dislikes is seeing cluttered bird cages so the birds have no straight lines to fly in to be able to get proper exercise and plastic perches instead of proper wooden ones of varying thickness that suit their feet. Pretty coloured ropes in bird cages too- the birds frequently nibble and then hang themselves in these- they should be banned. Budgies, parakeets and finches shouldn't be kept alone, they are social flock birds. But the saddest sight of all- quite common in some big pet stores as well as in private homes- is large tame Macaws confined to those small metal-barred 'prisons'- these I really hate.
Once again: a few of what you consider "good places for pets" might exist; this doesn't, however, negate the issue of a majority of inadequate private (and commercial) animal husbandry. As for good places for the precious polar bears and cetaceans "where animal needs are met and are in the best of care. the people that [ar]e there kn[o]w how to care for them and give them a great life": of course they exist. Zoochat is full of examples of good institutions and dedicated professional staff providing just that, and even more.